smc

By the Pythagorean Theorem, $(2x{)}^2+y^2=B{E}^2$, and $x^2+(2y{)}^2=A{D}^2$. Plugging in, $4x^2+y^2=16$, and $x^2+4y^2=49$. Adding the equations, $5x^2+5y^2=65$, and dividing by $5$, $x^2+y^2=13$. Note that the length $A{B}^2$ is equal to $(2x{)}^2+(2y{)}^2=4x^2+4y^2=4(x^2+y^2)$. Therefore, the answer is $\sqrt{4(13)}=2\sqrt{13}$ $\boxed{2\sqrt{13}}$